You need 27 tickets to guarantee a win on the UK National Lottery
arxiv.orgNot a "win" in the financial aspect of the game:
"... they matched just two balls on three of the tickets, the reward being three lucky dip tries on a subsequent lottery, each of which came to nothing. Since a ticket costs £2, the experiment represented a loss to the authors of £54.
This unfortunate incident therefore serves both as a verification of our result and of the principle that one should expect to lose money when gambling."
When I was young I had a friend who bought one Massachusetts (US) lottery ticket a week. I remember he "won" (basically got his money back). When he went to cash out the cashier asked him, "do you want the money.. or another ticket". He took the another ticket and promptly lost. lesson learned. You can't win if you don't play, but 2 tickets doesn't increase your odds significantly.
Where I worked there was a convenience store store. I got to know the owners a bit. One day they were posting a sign "People at our store won $850,000 on the lottery last year". I said, "wow thats a lot". She turned, shook her head and said "I know what they've spent... its not a lot." and proceeded into a mini tirade against gambling, which she promptly stopped when a customer entered the store. Its profitiable. But in the US with sports gambling everywhere, I wonder if lotteries have lost their luster.
There's a few Powerball Simulators (largest US lottery) out there - simulate buying 1 ticket a week indefinitely.
It usually works out to about a -90% ROI, though I did just somewhat undermine my point by hitting $2,000,000 (5 white balls + powerplay) after 246 years and becoming profitable. First time I've ever hit on one of these, I let one go for several millenia one time.
Of course, spending a few bucks per week isn't necessarily irrational. The hope and entertainment has some value.
And, of course, the marginal value of a couple bucks more in your pocket may be nil, but the life-changing experience of a win may have considerably more value; that is, marginal utility may not just flow smoothly downwards.
> isn't necessarily irrational
I used to say this to justify buying 20 tickets twice a week.
It's not irrational I can afford it, right? And the purchase gives me the psychological reward of dreaming about a big win.
But then after every draw I'd check my numbers and suffer a twinge of buyer's remorse. For me, that (small) regret more than offset any positive psychological benefit. It was a minor addiction that did more harm than good.
So now I've cured my addiction by turning Buyers Remorse into whatever the opposite of that is.
I have a cron job that generates 20 picks twice a week before each Mega Millions (US) draw.
I never buy these numbers -- the script just saves them in a Google Doc so there's evidence of the numbers and the timestamp when they were chosen.
Then after the draw, it checks them against the winning numbers, and emails me the results.
Now twice a week I get the (small) psychological benefit of realizing I didn't waste $40.
Maybe the opposite of Buyers Remorse is "Decliners Delight".
Wow, I hope that this cron job won't win anything significant. Imagine the remorse of nut buying those lucky numbers!
Everything's different for everyone.
I buy a few tickets every time the expected value might be weakly positive, even though this still doesn't make it a "good purchase."
And I've played blackjack under conditions (rules and my carefulness of play) where it's expected to be slightly money-losing, but had an exhilarating couple of hours and conversation. Cheap entertainment compared to many other things.
Anything in excess is bad. Having a couple drinks throughout your week is fine, going on a bender and downing 20 drinks one night per week isn’t.
Having a snickers bar is fine if you make it a rare reward, eating several every day isn’t.
Etc etc etc.
Isn't there another study of people that won big have also lost it/squandered it all within a fairly short amount of time?
Afaik (and I watch this fairly closely) there hasn't been a study. There are a lot of anecdotes, typically of the form "a person won a few million but spent like they had an income of a few million per year," sometimes of the form "a person won a huge amount of money but it turns out money doesn't solve all problems," and sometimes of the form "a person won a huge amount of money and invested it poorly." But most people who win a big lottery are still rich a decade or two later.
Even those who would be deemed "responsible" (already somewhat wealthy, otherwise stable) often end up far worse off.
It often ends in losing friendships, ties with family, death/kidnapping/blackmail threats both close and far away, endless frivolous lawsuits, financial ruin, etc.
The ratio of "happily ever after" stories to horror stories for winning the lottery seems a bit low for my tastes.
That’s just survivorship bias (or perhaps, the opposite).
You don’t hear the happily ever after stories because they don’t tend to reach out to the media after a few years and say “Hey! FYI I’m still rich and my life is perfect.”. They’re off enjoying their money somewhere. The scandals seem more common because those are the only situations that really get publicized.
>they don’t tend to reach out to the media after a few years and say “Hey! FYI I’m still rich and my life is perfect.”
No, that's what social media is for
Gamblers hardly intersects people who spend their money responsibly.
I believe the UK lottery has a required-by-law payout percentage of 42.47%.
28% also has to be donated to charity.
Which means, assuming you would donate to charity anyway, you are only wasting, on average, 30% of your money.
That is substantially better than the US powerball (at ~90%).
There is a point where the expected return is positive. Its around $1B or some large number like that. Sure the expected return is like 1% positive, but its positive.
Only if you don't factor in taxes and multiple winners.
This article added in sales numbers to estimate the actual expected value and it peaks around a $500 million jackpot with an expected value of $.85 from a $2.00 ticket. (very close to the bottom)
You can use the Kelly Criterion [0] to compute the optimum bet amount given the odds, the payoff, the cost of a ticket, and the size of your bankroll.
Usually the optimum bet is zero because the expected value is negative.
But when the jackpot gets big enough, occasionally the Kelly Criterion will advise buying a ticket or two if your bankroll is really big, like $10 million.
If the jackpot splits in the case of multiple winners, it's not positive - enough tickets will be bought until the expected number of winners is more than one and the expected value is no longer positive.
How does that work? By linearity of expectation, if the expected value of buying 1 ticket is negative then the expected value of buying multiple tickets should be even more negative
Typically lotteries roll over the jackpot if nobody wins. So if there's a streak of no winners, the total jackpot amount can be more than the cost of buying every possible ticket.
Of course, if you did this you might get unlucky and find that there's another winner in that draw, in which case you'd have to split the winnings and probably wouldn't make your money back.
The typical expected value of a lottery ticket is 50% of what you paid for it. That includes hitting the one-in-many-millions jackpot, which you could go many lifetimes without hitting. If it's given you don't hit the jackpot, then your expected value is much lower.
In your friend's case he increased his odds by 0. New ticket means a new game probably, so any prior winnings does not factor in the next game. He did increase his odds of losing everything significantly!
The rational thing to do is not play again. I'm sure someone can model this with game theory or probability math for us.
Stated another way. National and State lotteries are the largest ongoing wealth transfer from the lower-income bracket in the US. The lotteries are overwhelming played by the lower-income and that money is used to fund a large number of things in state governments.
> You can't win if you don't play, but 2 tickets doesn't increase your odds significantly.
Going from 0 to 1 tickets increases your odds infinitely. The spread on your possible outcomes goes from $0-0 to something like -$2 to $100m heavily weighted toward the bottom.
Going from 1 ticket to 2 tickets to 40 tickets… increases your odds by a very minuscule amount. The spread on your possible outcomes is now like -$80 to $100m, still heavily weighted towards the bottom.
The marginal value of every ticket after the first is basically negative.
I don’t buy lottery tickets but buying _one_ makes sense to me. No more than that.
That's the Law of Large Numbers working. A friend of mine won a small but not insignificant amount in a lottery and then "reinvested" it in the lottery and, as expected, lost it all.
>She turned, shook her head and said "I know what they've spent... its not a lot." and proceeded into a mini tirade against gambling, which she promptly stopped when a customer entered the store. Its profitiable.
Curious, but was this surprising to you? These games are literally all designed to take in money and pay out a portion of it. They have to be profitable.
I was surprised the payouts from a small convenience store were so high. And the spending were so high. I'm a very infrequent gambler..
When I was at IBM one of the mathemeticians had a bumper sticker on his office door. “the lottery: a tax on people who are bad at math.” or some such thing. I took it to heart.
Matt Parker video on the subject: https://youtu.be/zYkmIxS4ksA
It’s currently £2 per play so £54 for 27 tickets.
Matching two numbers on the last draw was rewarded with a £5 prize and a free lucky dip, but I think the £5 was only because it had rolled-over too many times.
27 support tickets? Like...
1: Hi there! Sorry to bother you but I think I have a winning ticket for the Powerbrits Billions Megapounds but I seem to have received an error at the cashier while checking my ticket...
2: Hi, me again! Yes, in response, I made sure the ticket was for the correct lottery. And yes, the cashier was listening to me when I asked them to check it...
3: Hello, hope you're well! I'm working on getting you that cashier screenshot as well as a picture of my ticket. Just wanted to reiterate I'm sure it's a winner, and there seems to be a bug in the code...
4: Hi there! Sorry I can't take a 'clearer picture with the ticket actually visible and readable' because that's the bug in the ticket I'm telling you about! Yes, again I'm sure it was a winner, I picked the numbers myself! And now I would not like a complimentary replacement ticket for the next drawing, thank you very much! Please don't close this support ticket as completed, too, alright? What I'd like is ...
[[ 21 support tickets later ]]
24: Hi friend! Yes, I'm quite sure the numbers on my ticket are 6-9-11-15-17-21, the exact numbers of the winning draw I'm hoping you'll help me collect! You can see from my recent photo that the 1 is clearly visible in a number of places and if you turn it to the left, you'll see what looks like a 5 and 7 as well. Clearly the rest of the positions have some bug where the numbers become unclear and appear to temporarily represent other numbers, but I didn't write them unclearly in the original (sorry I misplaced that!), so it is clearly a bug in your software! You know what, friend? F--- this, I have been nothing but reasonable. I think I might have to go to Hacker News and tell everybody about the terrible things that have happened as a result of this atrocious run around you've been giving me!
[[ 2 support tickets later ]]
27: Oh, hi, Senior Support Analyst Manager Derrick, thank you so much for your warm and accommodating email! Why, yes, that would be delightful, I will gladly accept monthly part-payments, less taxes, deposited into my standard Bank of Ireland (Maldives) account. Terribly good of you, if I say so myself! You have a fantastic day, Derrick! I'll be sure to fill out that little "Support Questionnaire" you sent me in your last correspondence, too (probably from St Tropez idk). Fantastic stuff!
I have a friend who once described state lotteries as “a tax on people who can’t do math”. That’s not particularly kind or fair. To me the combination of desperation that people feel that a lottery win would resolve a lot of their problems, and how many state-run programs are dependent on lottery funds to continue to function, is indicative of how bad an idea a lottery is.
It’s a trap for people who are desperate, trying to survive and a band-aid for a budget shortfall because people don’t want to pay taxes otherwise.
Matt Parker did a great video on this recently https://www.youtube.com/watch?v=zYkmIxS4ksA
On this theme, I really enjoyed the movie "Jerry and Marge go large" with Bryan Cranston. Based on a true story!
If you were going to run a syndicate with 27 entrants, would you be better off buying these 27 tickets or a random bunch of 27 tickets in terms of getting a jackpot?
Or is there no difference in terms of likelihood of getting a significant win?
This paper is focused on the little prizes. The odds of winning the jackpot will be the same for any play.
In fact the only thing you can do in the lottery is to avoid "popular" sequences like birthdays etc, so that if you do win you don't have to split it with a bunch of people.
A lottery in the Philippines famously had 433 winners, who all played 9, 18, 27, 36, 45 and 54. (https://www.cnn.com/2022/10/06/asia/philippines-grand-lotto-...)
The most disappointing thing here is that the number of winners wasn’t 432 or 423.
You have the best odds if you don't have overlapping numbers, so buying 27 deliberately is better than just getting random ones. That said, your xWin with just 27 tickets is still astronomically low.
I would probably avoid using these specific tickets; someone else may have had the same idea, and that means more likelyhood of prize sharing.
If you permute the numbers with a substitution cipher (randomly chosen), maybe? Personally, I'd prefer a ticket selection like this that covers all the numbers over 27 random selections that may leave some numbers open, etc; but I wouldn't be surprised if you run the numbers, assuming no prize sharing, and get the same results on any distinct 27 tickets.
These 27 ensure whatever gets pulled you will match two.
Or to put it another way, this system ensures you only lose £52 a week maximum before any additional free lucky dips or rolldowns.
It depends on what you're trying to optimize for, and how much you're trying to optimize it.
If what you're concerned about is maximizing the odds of getting a jackpot, all you need to do is pick 27 different numbers. Say, 1-2-3-4-5-6 through 1-2-3-4-5-32.
If what you're concerned about is maximizing the odds of getting a jackpot that you don't need to share with anyone else, you shouldn't play any numbers that you think anyone else is likely to play, such as the numbers in this paper, six numbers that form a straght line on the play slip (vertical, horizontal, or diagonal), any six consecutive numbers, the winning numbers from any recent drawing[1], or famous lottery numbers like 4-8-15-16-23-42 (the mystical numbers from the TV show "Lost.")
If what you're concerned about is guaranteeing a small win of some kind, then use some rotation of the numbers in this paper.
If what you're concerned about is minimizing the variance in the outcomes you achieve, then you'll want a more complicated formula for picking tickets, taking into account the values of the prizes for matching 2, 3, 4, 5, or 6 winning numbers. And if you're specifically looking for a set of tickets that's robust to operational interruptions in your ticket purchasing (what happens if the lottery system goes offline when you've bought ten of your 27 tickets, and you can't buy the last 17!?)[2].
But if one of the things you care about is the fully-loaded cost of buying 27 tickets, you'll almost certainly want to buy 27 random tickets, because picking specific numbers takes mental and physical effort, and 27 random tickets are unlikely to have enough overlap that it will have a significant impact on your likelihood of winning a large prize. The main downside of buying 27 random tickets is that it makes checking whether you won take more effort than if you already had your list of numbers.
And on that note, if what you care about is the fully-loaded cost of buying and redeeming your tickets, one of the best things you can do is the opposite of what this paper is about: you want to MINIMIZE the likelihood of winning a prize. Going to the store to cash a ticket takes effort, but it isn't much more effort to claim 27 prizes vs one single prize. So if you have a choice between a 1-in-27 chance of collecting 27 $2 prizes vs a 100% chance of collecting one $2 prize, you're better off with the former, simply because you can probably avoid an extra trip to the store.
[1] Unless you think there's a problem with the RNG system. IIRC about 15 years ago there was a state that drew the same lottery numbers 3 days in a row because they introduced a new computer PRNG and part of their runbook introduced the same seed for every draw; after the third consecutive draw they fixed the issue.
[2] I've had this happen to me, though the problem was that my bank froze my account partway through buying tickets, and I was buying a lot more than 27 tickets. The most famous/infamous lottery syndicate in modern history, a group from Australia that tried to buy every combination in the Virginia lottery in the early 1990s, also ran into logistical issues and was unable to finish buying their complete set of tickets, but they got lucky and hit the jackpot anyway.
This kind of thinking is also explored deeply in Jordan Ellenberg's book "How Not to be Wrong: The Power of Mathematical Thinking". Great read.
I've never purchased a lottery ticket but I do get a small reduction in my state property taxes from those who do, so I guess I win once a year.
I bought 3 tickets back in Nov 1994 when it started in England. I never won and never bought another ticket.
Ok
Not worth promoting mathmatical oddities that encourage people to gamble, in my opinion.
Surely you can't be serious. This site promotes social media companies all the time which you could easily argue is a much larger cause of problems in the world than gambling.
£2.00 * 27 is a guarantee to win something, with the most likely outcome a "Free Lucky Dip", or a £2.00 value. This is swaying no one's opinion.
They actually promote the opposite:
> For a more philosophical discussion of the National Lottery and its implementation for supporting charitable causes, we recommend David Runciman’s article in the London Review of Books
https://www.lrb.co.uk/the-paper/v18/n04/david-runciman/the-p...
crypto enters the chat.
The UK lottery does a lot of good with its funds and should be mentally separated from other betting/gambling firms in my opinion.
If you want to "gamble" its the best option, if you don't you can always wait for the government to inflate your cash away or spend it on Hilton rooms for sailors.
In no universe is the UK lottery good. All lotteries, the UK lottery included, are effectively sucking money out of the poor. It is profoundly, grotesquely regressive.
If the UK wanted to have an ethical, legitimate mechanism for distributing funds, it should levy a progressive tax that raises the same amount of money as the lottery.
Rishi already taxes the tits off anything he can recall after consuming half a tin of Dulux, please no more taxation.
My point isn't that the lottery is good, just that its the clear moral winner in an industry which includes Bet365, William hill, Coral and a million other pretenders.
If you want a small gamble and are adult enough to have financial independence its your best bet. If you don't or.. don't its totally optional.
> My point isn't that the lottery is good, just that its the clear moral winner in an industry which includes Bet365, William hill, Coral and a million other pretenders.
That's like saying burglary is the clear moral winner over murder. While we all would prefer to be burgled than murdered, I think it's fair to say that burglary is very, very bad.
No. It does "good" with about 25% of it's income. A lot of that "good" is stuff that the government or local councils would just fund directly if the Lottery wasn't paying for them. Much better to just give money to your favourite charity directly.
>Much better to just give money to your favourite charity directly.
Checking the (published) 'admin costs' vs actual donated/ used monies is a great way to pick favorites.
I disagree. I'd argue that Wikipedia or the Internet Archive are 100% admin, and that's a good thing. I don't want them spending money paying people to write articles or paying people to add stuff to the archive.
There are a lot of charities in between where some more money on admin (e.g. better training, better organisation) can make the front line workers more effective.
If you want to "gamble" its the best option
The national lottery has an expected return of roughly 50% of your bet. They give about 30% of your bet to charity. So if you gamble £100, you'll end up with £50 in your pocket and £30 donated to charity.
Blackjack on the other hand returns roughly 90% of your bets over time if you play well. So if you donate £40 to charity and take the remaining £60 to a blackjack table you'll end up with more money going to charity and with more money in your pocket.
> take the remaining £60 to a blackjack table
Of course, "take the remaining 60 pounds" is ill-posed; what does that mean, make 60 bets of 1 pound and stop? Play a single 60 pound bet hand? Because that's the conditions under which you could expect to bring 60 and typically leave with ~54.
If you show up with 60 pounds but bet well over 60 cumulatively you're going to end up with much less.